Effective Maxwell’s equations in general periodic microstructures

ABSTRACT

We study the time harmonic Maxwell equations in a meta-material consisting of perfect conductors and void space. The meta-material is assumed to be periodic with period ; we study the behaviour of solutions in the limit and derive an effective system. In geometries with a non-trivial topology, the limit system implies that certain components of the effective fields vanish. We identify the corresponding effective system and can predict, from topological properties of the meta-material, whether or not it permits the propagation of waves.

KEYWORDS:

• Maxwell’s equations
• homogenisation
• diffraction
• periodic structure
• meta-material

AMS SUBJECT CLASSIFICATIONS:

• 35Q61
• 35B27
• 78M40
• 78A45

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Support of both authors by DFG [grant number Schw 639/6-1] is gratefully acknowledged.